arXiv research

Construct opers with apparent singularities from λ-connections on Riemann surfaces.

Investigate the local geometry of smooth surfaces in 4-space via contact with 2-planes and apparent contours.

New method proves instability of naked singularity and censors it.

Researchers determine all possible representations of monodromy for Schwarzian equations on punctured surfaces.

We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We a…

We study Jang's equation on a one-parameter family of asymptotically flat, spherically symmetric Cauchy hypersurfaces in the maximally extended Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are parametrized by their proximity to the singularity at $r = 0$. We show that on those hypersurfaces …

We determine the precise bifurcation diagrams of the apparent contours of generic crosscaps, which contain the information of bifurcations with respect to the images of the singular sets of crosscaps: crosscap points and double point curves. Especially, three different kinds of equivalences play key roles.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

Generalizes isomonodromic-isospectral correspondence for twisted connections.

The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event …

We study the geometry of the cuspidal edge $M$ in $\mathbb R^3$ derived from its contact with planes and lines (referred to as flat geometry). The contact of $M$ with planes is measured by the singularities of the height functions on $M$. We classify submersions on a model of $M$ by diffeomorphisms and recover the cont…

We construct a Legendrian version of Envelope theory. A tangential family is a 1-parameter family of rays emanating tangentially from a smooth plane curve. The Legendrian graph of the family is the union of the Legendrian lifts of the family curves in the projectivized cotangent bundle $PT^*\R^2$. We study the singular…

Paper studies apparent horizon dynamics and introduces a null comparison principle.

Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which, under a set of conditions, allow us to define proper geometric invariants, and to w…

Kernel networks' stability edge linked to Fisher Information singularity.

Introduces LLC, a new complexity measure for DNNs based on SLT.

In this paper we characterize the intrinsic geometry of apparent horizons (outermost marginally outer trapped surfaces) in asymptotically flat spacetimes; that is, the Riemannian metrics on the two sphere which can arise. Furthermore we determine the minimal ADM mass of a spacetime containing such an apparent horizon. …

Solves Einstein constraint equations on compact manifolds with specified boundaries.

In this paper we find new examples of Riemannian manifolds with outermost apparent horizons with nonspherical topology, in dimensions four and above. More precisely, for any $n,m\ge1$, we construct asymptotically flat, scalar flat Riemannian manifolds containing smooth outermost minimal hypersurfaces with topology $S^n…

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal projections in a number of directions. We discuss relations between (1) a space c…

Paper analyzes blowup of regularized Jang solutions and constant expansion surfaces.

This note shows surfaces in stable 3D data are bounded by area and diameter.

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.

This paper generalizes monodromy maps for projective structures with poles.

Constructs initial data leading to apparent horizons and tests Penrose Inequality.

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space.

Given a submanifold $S \subset \mathbb R^n$ of codimension at least three, we construct an asymptotically Euclidean Riemannian metric on $\mathbb R^n$ with nonnegative scalar curvature for which the outermost apparent horizon is diffeomorphic to the unit normal bundle of $S$.

The paper shows how to create Schwarzschild initial data with degenerate apparent horizons.

For a punctured surface $S$, we characterize the representations of its fundamental group into $\mathrm{PSL}_2 (\mathbb{C})$ that arise as the monodromy of a meromorphic projective structure on $S$ with poles of order at most two and no apparent singularities. This proves the analogue of a theorem of Gallo-Kapovich-Mar…

The paper studies curves in surfaces using flow-spines and apparent contours.

Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.

In this paper we will try to assess the multifractality displayed by the high-frequency returns of Madrid's Stock Exchange IBEX35 index. A Multifractal Detrended Fluctuation Analysis shows that this index has a wide singularity spectrum which is most likely caused by its long memory. Our findings also show that this lo…

Reducing volatility proxy improves apparent market correlation dynamics.

We propose a method to classify cardiac pathology based on a novel approach to extract image derived features to characterize the shape and motion of the heart. An original semi-supervised learning procedure, which makes efficient use of a large amount of non-segmented images and a small amount of images segmented manu…

Generalizes Rips' result on hyperbolic spaces to metric spaces, showing collapses for tree metrics.

Perceived personality traits attributed to an individual do not have to correspond to their actual personality traits and may be determined in part by the context in which one encounters a person. These apparent traits determine, to a large extent, how other people will behave towards them. Deep neural networks are inc…

We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method used by Ise…

New method normalizes Milnor fibrations for real analytic maps.

New method transfers causal mechanisms for few-shot domain adaptation.

Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.

Bartnik mass is positive and non-decreasing for black holes

The paper addresses causal estimation for text data with apparent overlap violations.

In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the Markov-switching multifractal model (MSM). In order to see how well the estimated models captur…

Risk-only investment strategies have been growing in popularity as traditional in- vestment strategies have fallen short of return targets over the last decade. However, risk-based investors should be aware of four things. First, theoretical considerations and empirical studies show that apparently dictinct risk-based …

Suppose curves are moving by curvature in a plane, but one embeds the plane in $R^3$ and looks at the plane from an angle. Then circles shrinking to a round point would appear to be ellipses shrinking to an ``elliptical point,'' and the surface energy would appear to be anisotropic as would the mobility. The result of …

Study examines Wang-Yau quasi-local energy in strong fields near apparent horizons.

A distinction has been drawn in fair machine learning research between `group' and `individual' fairness measures. Many technical research papers assume that both are important, but conflicting, and propose ways to minimise the trade-offs between these measures. This paper argues that this apparent conflict is based on…

Develops graphical calculus for monoidal categories with twisted pivotal structures.